N = 8   -- board size

-- check whether position(n,c) is free from attacks
function isplaceok(a, n, c)
    for i = 1, n - 1 do     -- for each queen already placed
        if (a[i] == c) or               -- same column?
           (a[i] - i == c - n) or       -- same diagonal?
           (a[i] + i == c + n) then     -- same diagonal? 
            return false    -- place can be attacked
        end
    end

    return true
end


-- print a board
function printsolution(a)
    for i = 1, N do     -- for each row
        for j = 1, N do     -- and for each column
            -- write "X" or "-" plus a space
            io.write(a[i] == j and "X" or "-", " ")
            io.flush()
        end
        io.write("\n")
        io.flush()
    end
    io.write("\n")
    io.flush()
end

-- add to board 'a' all queens from 'n' to 'N'
function addqueen(a, n)
    if n > N then -- all queens have been placed?
        printsolution(a)
    else -- try to place n-th queen
        for c = 1, N do
            if isplaceok(a, n, c) then
                a[n] = c -- place n-th queen at column 'c'
                addqueen(a, n+1)
            end
        end
    end
end

-- run the program
addqueen({}, 1)